Yes, California has that authority, and understanding why helps clarify what the path forward actually looks like.
When someone is on parole or probation, the supervising state is legally responsible for monitoring their conduct and whereabouts for the duration of the supervised release period. That responsibility does not automatically transfer just because the family lives elsewhere or because restitution has been paid. California retains jurisdiction over where he lives and works until supervision is complete, and they take that responsibility seriously.
That said, transferring supervision to Alabama is a legitimate and commonly used process. It is governed by the Interstate Compact for Adult Offender Supervision, an agreement between all 50 states that provides a formal mechanism for exactly this situation. California would initiate a transfer request, Alabama would investigate whether accepting supervision serves the public interest, and if Alabama approves it, supervision transfers and he reports to an Alabama officer rather than a California one.
The factors that help Alabama say yes are the same ones that help any transfer request. A verified stable address with family, the absence of any conditions tied to the conviction that make the proposed residence unsuitable, and a clean supervision record that makes him a low-risk transfer candidate all strengthen the application.
The paid restitution is a positive factor but it does not override the transfer process. His California parole or probation officer is the starting point for initiating the request. That conversation should happen as soon as possible, and having documentation of the family residence in Alabama ready to submit with the application moves things along faster.